algebra

It takes 7 hours for Isabella to rake leaves by herself.Her brother can work 3 times as fast.if they work together,how long will its take them to rake leaves?

My answer: Isabella can do one job in 7 hours (1/7in one hour).Matthew does 3/4 of the job in one hour. Together they do 1/7 + 3/7 =4/7 of the job in one hour. They do the entire job in 7/4 or 1.75 hours.

My question: how do I show just the Rate,Time,and Work Done by each person?

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  1. t1 = 7 hrs.
    t2 = 1/3 * 7 = 7/3 hrs.

    T = t1*t2/(t1+t2) = (7*7/3)/(7+7/3).
    T = (49/3)/(28/3)
    T = 49/3 * 3/28 = 49/28 = 7/4 = 1.75 hrs.

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    posted by Henry
  2. Another Method:
    t1 = 7 hrs.
    t2 = 1/3 * 7 = 7/3 hrs.

    1/T = 1/t1 + 1/t2.
    1/T = 1/7 + 3/7 = 4/7,
    T = 7/4 = 1.75 hrs.

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    posted by Henry

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